Very recent studies performed by the authors have shown that the use of the new triisopropylgallium (TiPGa) precursor leads to an important order-of-magnitude reduction in unintentional carbon impurity levels in GaAs layers grown by chemical beam epitaxy (CBE), when compared with layers grown using triethylgallium (TEGa). The present paper provides additional GaAs growth data, particularly relating to the layer growth rate dependence on substrate temperature, and then describes the first reported use of TiPGa for Ga1-xAlxAs CBE growth. When used in combination with alane trimethylamine, the TiPGa precursor again leads to significant reductions in unintentionally incorporated carbon impurity levels in the resulting Ga0.7Al0.3As CBE layers, compared with corresponding TEGa-grown material. Initial GaAs/Ga1-xAlxAs two-dimensional electron gas (2DEG) structures have also been grown and have already exhibited 77 K and 4 K 2DEG mobility values of 62 000 cm2 V-1 s-1 and 104 000 cm2 V-1 s-1 respectively.